Key Ideas

Key Ideas from Chapter 1: 

The Six Principles for School Mathematics

• The Equity Principle
• The Curriculum Principle
• The Teaching Principle 
• The Learning Principle
• The Assessment Principle
• The Technology Principle

The Five Process Standards for School Mathematics 

• Problem Solving Standard
• Reasoning and Proof Standard
• Communication Standard
• Connections Standard
• Representation Standard

Six Major Necessary Components for Students to Develop Mathematical Understanding

Create an environment that offers equal opportunities for all to learn

Focus on a balance of conceptual understanding and procedural fluency 

Ensure active student engagement in the NCTM process standards

Use technology to enhance understanding

Incorporate multiple assessments aligned with instructional goals and mathematical practices

Help students recognise the power of sound reasoning and mathematical intergrity

Key Ideas from Chapter 2:

The Classroom Environment for Doing Mathematics

• Persistence, effort and concentration are important in learning mathematics
• Students share their ideas
• Students listen to each other
• Errors are opportunities for learning 
• Students look for and discuss connections

Problem Based Teaching Strategies formed by Constructivist and Socialcultural Perspectives

Build New Knowledge from Prior Knowledge

Provide Opportunities to Discuss Mathematics

Build in Opportunities for Reflective Thought

Encourage Multiple Approaches

Engage Students in Productive Struggle

Treat Errors as Opportunities for Learning

Scaffold New Content

Honor Diversity

Strands of Mathematical Proficiency

Conceptual Understanding: Comprehension of mathematical concepts, operations and relations

Procedural Fluency: Skill in carrying out procedures flexibly, accurately, efficiently and appropriately

Strategic Competence: Ability to formulate, represent, and solve mathematical problems

Adaptive Reasoning: Capacity for logical thought, reflection, explanation and justification

Productive Disposition: Habitual inclination to see mathematics as sensible, useful and worthwhile, coupled with a belief in diligence and one's own efficacy